Related papers: Three Problems of "Distinction"
Cardinality constraints are important in many Sat problems; previous studies provide contradictory conclusions about the best encoding to use. Here, three encodings are compared: Sinz's sequential-counter, Bailleux and Boufkhad's…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
We study the triangle inequalities for angles (with different definitions) and present inequalities concerning the entries of correlation matrices through the positivity of $3\times 3$ matrices. We extend our discussions to the inequalities…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
This work lies across three areas (in the title) of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link consists of a single…
The two closely related Lorentz-invariant partial orders of space-time are distinguished with respect to the existence of antichain cutsets and the possibility of grading. World lines of particles with or without mass are the maximal chains…
Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders (tau-covers). We deal with two types of combinatorial questions which arise from this study. 1.…
We present an account of different problems that arise in relation with cyclicity problems in Dirichlet-type spaces, in particular with polynomials $p$ that minimize the norm $\|pf-1\|$.
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is…
Analogical proportions compare pairs of items (a, b) and (c, d) in terms of their differences and similarities. They play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
The topic is the history of the concepts of equivalence relation, Cauchy sequence, and metric space. The thesis is that disused definitions of these notions could profitably be revived.
We address the problem of computing distances between rankings that take into account similarities between candidates. The need for evaluating such distances is governed by applications as diverse as rank aggregation, bioinformatics, social…
(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…
In this article we study relationship between three measures of distinguishability of quantum states called as divergence, relative entropy and the substate property.
Lines and circles pose significant scalability challenges in synthetic geometry. A line with $n$ points implies ${n \choose 3}$ collinearity atoms, or alternatively, when lines are represented as functions, equality among ${n \choose 2}$…
The problem of equivalency for linear differential operators of the first order is discussed.
We introduce the split principles and show that they bear tight connections to large cardinal properties such as inaccessibility, weak compactness, subtlety, almost ineffability and ineffability, as well as classical combinatorial objects…
The main contribution of this dissertation is the introduction of new or improved approximation algorithms and data structures for several similarity search problems. We examine the furthest neighbor query, the annulus query, distance…
The almost disjointness numbers associated to the quotients determined by the transfinite products of the ideal of finite sets are investigated. A $\mathrm{ZFC}$ lower bound involving the minimum of the classical almost disjointness and…